After the rather difficult pi challenge, I thought I'd propose another (hopefully) easier challenge. This time we're after the golden ratio, phi, which is approximately 1.6180339887...

Now, the obvious six command / seven keystroke sequence on the 12c is:

5 g-sqrt 1 + 2 /

This results in 1.618033989 on the display (assume FIX 9 is already set). I think it would be difficult to better this but I would be very interested in a shorter sequence if such is found.

However, let us presume for some unknown reason that we want the resulting digits correct and unrounded. That is, we want 1.618033988 on the display. Now clearly this can be done in four additional steps/keystrokes with

5 sqrt 1 + 2 / EEX 9 CHS -

However, it can be done with fewer. Specifically, it can be done in at most the same number of operations and keystrokes as the correctly rounded version I gave initially. That is, six operations maximum and seven keystrokes maximum.

So how is it best suited for trig functions (for example)? It takes pretty much a long set of keystrokes to emulate predefined trig functions in the scientific calculators. I learned that it is better to work smarter than harder.